Distinct beta frequencies reflect categorical decisions

Based on prior findings of content-specific beta synchronization in working memory and decision making, we hypothesized that beta oscillations support the (re-)activation of cortical representations by mediating neural ensemble formation. We found that beta activity in monkey dorsolateral prefrontal cortex (dlPFC) and pre-supplementary motor area (preSMA) reflects the content of a stimulus in relation to the task context, regardless of its objective properties. In duration- and distance-categorization tasks, we changed the boundary between categories from one block of trials to the next. We found that two distinct beta-band frequencies were consistently associated with the two relative categories, with activity in these bands predicting the animals’ responses. We characterized beta at these frequencies as transient bursts, and showed that dlPFC and preSMA are connected via these distinct frequency channels. These results support the role of beta in forming neural ensembles, and further show that such ensembles synchronize at different beta frequencies.

1. All the findings related to dlPFC, in particular Figure 4, rely on one monkey. While the granger causality analysis is interesting as an exploratory finding, one should take caution in concluding anything from it given that it came from one monkey. As such, I recommend de-emphasizing the dlPFC findings from the abstract and the text.
2. While the consistency in frequency shift between distance and duration for the representation of short vs long categories is highly interesting, it's not clear how. Perhaps "short" category is represented with a smaller ensemble, and synchronizes at a faster frequency? Or maybe the neurons representing the "short" category has a higher firing rate during the decision delay period and this leads to higher beta frequency? Some discussion on plausible biophysical mechanisms would be helpful and interesting to the readers.
Medium-level Comments 1. The experimental design is very elegant in that the same exact interval and distance values could be short in one block and long in another block. However, there is no direct comparison of these overlapping values in different blocks. It would be very powerful to show the frequency effects for identical stimuli in different blocks (e.g., 450 or 500ms trials for T1 block vs T2 block).
Minor Comments 1. In the spatial task, was the first and second stimulus within a trial identical? Please clarify.
2. In the Introduction, it would be helpful to mention why the authors chose to record from dlPFC and preSMA during this categorization task.
Reviewer #2 (Remarks to the Author): This study presents an analysis of electrophysiological recordings from macaque pre-SMA and dlPFC during two magnitude categorization tasks (one based on temporal interval, the other on spatial intervals). The authors compute frequency spectra of local LFP power, inter-area LFP coherence, and within-area spike-field coherence between and compare them between long vs. short category trials. They also compare spectra of inter-area Granger causality, in both directions (preSMA -Y dlPFC and vice versa). The main finding is a peak shift between long vs. short judgments for the spectra of all the above measures, specifically within the beta frequency range (the most prominent peak in the overall power spectra). For LFP power, this peak shift also reflects the reported judgment rather than the stimulus (i.e., flipping with respect to stimulus category for error trials) and is categorical in nature, rather than reflecting the continuous differences present in the stimuli.
I found the reported effects to be interesting, and the methods are sound. At the same time, the study seems to have conceptual shortcomings and the analyses presented seems to be somewhat incomplete.
1. The study falls short of providing an account for how the peak frequency of LFP oscillations should encode categorical decisions about magnitude. How does this peak shift come about, and how is it read out downstream to drive behavioral choice? A simple model could help here.
2. Relatedly, the study by Mendoza et al, Nat Commun (2018) provided a beautiful and careful analysis of the encoding of stimulus categories and animals' decisions in the firing rate dynamics of individual preSMA neurons in these tasks. The current paper would be a lot more impactful if it related the current LFP analyses more directly to those of the spiking activity, in terms of their functional properties (which information is present in spiking that is not present in the LFP spectra) as well as in terms of their correlation (i.e., spike-field coherence, currently only shown for dlPFC, not preSMA).
3. The authors claim that the results are the same for the temporal and spatial tasks, but all spectra shown in the main figures are collapsed across both tasks. There seems to be some information about the estimated peak parameters for the individual tasks in the supplementary tables (unclear, due to use of shorthands for the conditions which are not defined), but this is not sufficient to evaluate the effects. Please show separate spectra for the two tasks.
4. It is unclear whether the inter-area coherence and Granger causality effects reflect the stimulus or the categorical judgments. The error analyses should also be done for these measures.
5. The authors claim that the peak frequency shift emerges from the beta frequency drive from dLPFC to preSMA. But the peak shifts are visible in the spectra for both directions, they are just not statistically significant for the direction preSMA -> dlPFC. To make a stronger case about the origin of the effect, the authors should quantitatively compare the beta peak shifts between the two directions (dlPFC -> preSMA -vs. preSMA -> dlPFC).

Minor:
Is this a re-analysis of the data from Mendoza et al, Nat Commun (2018)? I haven't found an explicit statement about this anywhere in Methods. I applaud efforts to re-analyze such datasets for multiple independent studies. But it is important to be clear and transparent about this.
1. All the findings related to dlPFC, in particular Figure 4, rely on one monkey. While the granger causality analysis is interesting as an exploratory finding, one should take caution in concluding anything from it given that it came from one monkey. As such, I recommend de-emphasizing the dlPFC findings from the abstract and the text.
We agree with the reviewer that caution is warranted when it comes to interpreting the findings related to dlPFC, as they rely on one monkey. Unfortunately, dlPFC data was not available from the second monkey. As such, we have now de-emphasized these findings in the abstract, results, and discussion sections. We have additionally clarified in the results and discussion sections that since dlPFC data was only available for one monkey, those findings should be considered tentative and not conclusive.
Results, page 7 "Note that these simultaneous recordings were only available in one animal, so the following results should be treated with caution." page 8: "However, we cannot draw strong conclusions from the above results relating to connectivity and spike-field coherence, as these results rely on data from one animal." Discussion, page 12: "Top-down prefrontal signals have also previously been reported in the parietoprefrontal circuit during spatial categorization in the monkey 27,28 ; however the current results are based on one animal." 2. While the consistency in frequency shift between distance and duration for the representation of short vs long categories is highly interesting, it's not clear how. Perhaps "short" category is represented with a smaller ensemble, and synchronizes at a faster frequency? Or maybe the neurons representing the "short" category has a higher firing rate during the decision delay period and this leads to higher beta frequency? Some discussion on plausible biophysical mechanisms would be helpful and interesting to the readers.
We thank the reviewer for thinking along about the plausible biophysical mechanisms that lead to the frequency shift. We were not able to verify that "short" category is represented with a smaller ensemble, as there were on average more short-selective cells than long-selective cells in our sample. We also observed no differences in the average firing rates of short-and long-selective cells. We now report these observations descriptively in the text but do not draw conclusions from them. Instead, we offer a plausible biophysical mechanism for how the frequency shift is generated based on the modelling work in Sherman et al. (2016, PNAS), and a plausible algorithmic mechanism of how it is transmitted downstream based on the modelling work in Akam & Kullman (2014, Nat Rev Neurosci). Finally, we speculate that the consistency in frequency shift between distance and duration tasks is likely because the downstream consequence of the frequency shift is the same in both cases (i.e., producing behavior corresponding to "long" or "short" categorization).
Note that there were no significant differences in the firing rates of these "short" vs "long" cells (both t<1, both p>.3)." Discussion, page 12: "Biophysically, a plausible account of how beta could emerge at different frequencies is provided by Sherman and colleagues 20 , who found that beta events emerge in cortex when synchronous bursts of subthreshold excitatory synaptic input are simultaneously integrated by proximal and distal dendrites of pyramidal neurons. If the distal input is sufficiently strong and lasts about a beta period, a beta burst can be generated. The duration of this distal drive was shown to be linearly correlated with the period of the beta burst, so inversely related to its frequency. The source of the distal drive is possibly the ventromedial thalamus, known to project to supragranular layers in prefrontal cortex 29 . This pathway has been shown to modulate the overall activity of the recipient area without eliciting spikes 30 .
Prominent theoretical accounts of the function of neural oscillations propose that oscillations control the flow of signals between anatomically connected regions 31 . At the algorithmic level, beta oscillations at different frequencies could act as separate channels to selectively transmit decision information downstream, referred to in a model by Akam and Kullman as frequency-division multiplexing 32,33 . Once a neural population code encodes a decision, an oscillation at a particular frequency can serve as a channel to selectively transmit the code downstream, where a network with the appropriate filter settings can selectively read out the code 33 . Transient oscillatory bursts at distinct frequencies, as observed in our data, are particularly well-suited for this mechanism 32 . In this view, the neural population code represents the value of the signal, while the oscillatory modulation represents the metadata required to distinguish the signal from others.
Previous accounts had proposed a role for beta in maintaining mental content 16 . Recently, we proposed that beyond maintenance, beta plays a role in reactivating latent contents 15 . Here, we provide support for this account. In this experiment, the relative categories were defined at the start of each session, and this content was then reactivated during each trial's decision delay in order to correctly perform the task. With the contents likely coded at the level of neurons 11,34 , we propose that beta oscillations play a role in selectively (re-)activating the relevant neural ensembles at the right moments, and selectively relaying their signals downstream. Our observation that the frequency shift is consistent between the distance and duration tasks supports this view: because the downstream consequences of the decision signals are the same in both temporal and spatial versions of our task (i.e., producing behavior corresponding to "long" or "short"), the decision signals are transmitted within the same frequency channels in both task versions."

Medium-level Comments
1. The experimental design is very elegant in that the same exact interval and distance values could be short in one block and long in another block. However, there is no direct comparison of these overlapping values in different blocks. It would be very powerful to show the frequency effects for identical stimuli in different blocks (e.g., 450 or 500ms trials for T1 block vs T2 block).
We apologize that the contrast for identical stimuli in different blocks was perhaps not sufficiently highlighted in the text. We had reported this in the results section "Two distinct beta-band frequencies reflected the two relative categorical decisions across tasks and recording sites", (page 6, third paragraph), referring to the relevant stimuli as "very long" and "very short". We reported this finding for both T1 vs T2 and T2 vs T3; however, in re-reading the section, we realized there were typos in that paragraph which might have made the section unclear. We have now corrected the typos. Note that in the main text, we pooled across the two longest stimuli in T1 and the two shortest in T2 (i.e., 450ms and 500ms) and did the same for the T2 and T3, resulting in two contrasts per region. We have now additionally included the contrasts for each individual overlapping stimulus (i.e., 450ms and 500ms separately) as Tables 9 (dlPFC) and 10 (preSMA).  Table 9. Beta frequency shift in dlPFC during decision delay of the duration categorization tasks, for trials with identical stimuli within different task versions (i.e., trials with identical stimuli categorized as "short" in one task version but "long" in another; see overlapping stimuli outlined in Figure 1b).  29.6 (+/-2.0) 2.9, 82 .005 Table 10. Beta frequency shift in preSMA during decision delay of the duration categorization tasks, for trials with identical stimuli within different task versions (i.e., trials with identical stimuli categorized as "short" in one task version but "long" in another; see overlapping stimuli outlined in Figure 1b). Table 5 and Table 7 equivalents for each monkey. Even if the frequency shift effects are not significant for both monkeys, it would be important to confirm that the effects are in the same direction.

I recommend including
Indeed, the frequency shift effect is significant for both monkeys. However, since monkey 2 data is only available for 18 sessions (~3 sessions x 6 tasks), it would not be very meaningful to split monkey 2's data into the 6 different tasks. Instead, we have added a row to Table 5 aggregating the data from monkey 2, and removed monkey 2's data from the remaining rows, which now represent monkey 1's data. We've also added the .016 Table 5. Beta frequency shift in preSMA during decision delay for trials categorized as "short" vs. "long". T1, T2, and T3 are the interval categorization tasks with the shortest, middle, and longest sets of intervals, respectively (see Figure 1b for exact values). S2 is the distance categorization task with the middle set of distances. For Monkey 2, tasks additionally included S1 and S3, the distance categorization tasks with the shortest and longest distances, respectively.  Table 8. Beta burst profile in Monkey 2 preSMA during decision delay for trials categorized as "short" vs. "long". All t-value df = 17.

With the p-values and t-values
, it is difficult to infer the effect size. Some measure of effect size (e.g., AUROC when using frequency to predict monkey's decision) would be helpful. This is a good suggestion. Using frequency to predict monkeys' decisions, we obtained AUROC of .751 for monkey 1 dlPFC, .724 for monkey 1 preSMA, and .660 for monkey 2 preSMA.
Note that these values do not represent predictions for monkeys' decisions on a single-trial basis. Because frequency spectra at the single-trial level are very noisy, our unit of observation for statistics throughout the manuscript was at the session level. We applied the same logic here, averaging the spectra separately for each decision within a session, before fitting a logistic regression with frequency as predictor.
We have now added the AUROC values to the main text (Results, pages 5 and 6) , and explained how we obtained these values in the Methods section (Spectral analysis, page 15): "In addition, for this effect of peak frequency on decisions, we quantified effect size with Area Under the Receiver Operating Characteristics (AUROC). We fit a logistic regression with the averaged spectra as predictors and the decisions as response variables, before computing the area under the ROC curve, using the probability estimates from the logistic regression model as scores." 4. In Figure 4, spike-field coherence panel for preSMA is missing?
We had originally chosen not to show the preSMA data as there was no clear pattern in those data. We have now included a figure of spike-field coherence in preSMA for completeness. We also corrected an error in the way we had plotted the shaded error regions of the dlPFC spike-field coherence data. Figure S5. Spike-field coherence during the decision delay. (a) Spike-field coherence in dlPFC between short-selective neurons and the LFP during short-categorized trials, and between longselective neurons and the LFP during long-categorized trials: the peak frequency reflected the categorical decision. (b) Same for preSMA: there were no significant peaks in the beta range.

Minor Comments
1. In the spatial task, was the first and second stimulus within a trial identical? Please clarify. Yes, in both task versions, the first and second stimuli were identical within a trial. This is now clarified in the first paragraph of the Results section (page 3).

"Although the distance between bars varied between trials in the spatial task, it was identical within a trial in both task versions."
2. In the Introduction, it would be helpful to mention why the authors chose to record from dlPFC and preSMA during this categorization task.
Thank you for the suggestion. We have added the following sentences in the introduction (page 2): "dlPFC is known to play a central role in categorization 12 and is part of the magnitude system for time, space, and quantity 13 . It is deeply connected with preSMA, which is known to be a major node in the time processing network 14 , and contains cells that have been shown to encode the boundary between categories 11 ."

Response to Reviewer 2
Major 1. The study falls short of providing an account for how the peak frequency of LFP oscillations should encode categorical decisions about magnitude. How does this peak shift come about, and how is it read out downstream to drive behavioral choice? A simple model could help here.
We agree with the reviewer that more discussion of the relationship between peak frequency and categorical decisions is warranted. We would like to first clarify that we do not claim that the LFP encodes decisions. Most likely the categorical decisions are encoded (in spike firing patterns) by boundary cells and category-selective cells as elegantly shown by Mendoza et al., 2018. What we observe in the LFP peak frequency is a signal that reflects the decision, likely a channel to transmit the decision downstream. We now offer a plausible biophysical mechanism for how the frequency shift is generated based on the modelling work in Sherman et al. (2016, PNAS), and a plausible algorithmic mechanism of how it is transmitted downstream based on the modelling work in Akam & Kullman (2014, Nat Rev Neurosci).

Discussion, page 12:
"Biophysically, a plausible account of how beta could emerge at different frequencies is provided by Sherman and colleagues 20 , who found that beta events emerge in cortex when synchronous bursts of subthreshold excitatory synaptic input are simultaneously integrated by proximal and distal dendrites of pyramidal neurons. If the distal input is sufficiently strong and lasts about a beta period, a beta burst can be generated. The duration of this distal drive was shown to be linearly correlated with the period of the beta burst, so inversely related to its frequency. The source of the distal drive is possibly the ventromedial thalamus, known to project to supragranular layers in prefrontal cortex 29 . This pathway has been shown to modulate the overall activity of the recipient area without eliciting spikes 30 .
Prominent theoretical accounts of the function of neural oscillations propose that oscillations control the flow of signals between anatomically connected regions 31 . At the algorithmic level, beta oscillations at different frequencies could act as separate channels to selectively transmit decision information downstream, referred to in a model by Akam and Kullman as frequency-division multiplexing 32,33 . Once a neural population code encodes a decision, an oscillation at a particular frequency can serve as a channel to selectively transmit the code downstream, where a network with the appropriate filter settings can selectively read out the code 33 . Transient oscillatory bursts at distinct frequencies, as observed in our data, are particularly well-suited for this mechanism 32 . In this view, the neural population code represents the value of the signal, while the oscillatory modulation represents the metadata required to distinguish the signal from others.
Previous accounts had proposed a role for beta in maintaining mental content 16 . Recently, we proposed that beyond maintenance, beta plays a role in reactivating latent contents 15 . Here, we provide support for this account. In this experiment, the relative categories were defined at the start of each session, and this content was then reactivated during each trial's decision delay in order to correctly perform the task. With the contents likely coded at the level of neurons 11,34 , we propose that beta oscillations play a role in selectively (re-)activating the relevant neural ensembles at the right moments, and selectively relaying their signals downstream. Our observation that the frequency shift is consistent between the distance and duration tasks supports this view: because the downstream consequences of the decision signals are the same in both temporal and spatial versions of our task (i.e., producing behavior 2. Relatedly, the study by Mendoza et al, Nat Commun (2018) provided a beautiful and careful analysis of the encoding of stimulus categories and animals' decisions in the firing rate dynamics of individual preSMA neurons in these tasks. The current paper would be a lot more impactful if it related the current LFP analyses more directly to those of the spiking activity, in terms of their functional properties (which information is present in spiking that is not present in the LFP spectra) as well as in terms of their correlation (i.e., spike-field coherence, currently only shown for dlPFC, not preSMA).
We thank the reviewer for helping us elaborate on points that will make our paper more impactful. We think our response to the previous comment addresses the current comment regarding the functional properties of spikes and LFP. We would like to add that the LFP provides a network-level source of information that can be translated to non-invasively recorded signals (EEG or MEG). There is no noninvasively recorded signal that corresponds to spiking activity. In that sense, experiments on healthy human populations can more directly benefit from insights gained by analyzing LFP spectra.
Regarding spike-field coherence, we had originally chosen not to show the preSMA data as there was no clear pattern in those data. We have now included a figure of spike-field coherence in preSMA for completeness. We also corrected an error in the way we had plotted the shaded error regions of the dlPFC spike-field coherence data. Figure S5. Spike-field coherence during the decision delay. (a) Spike-field coherence in dlPFC between short-selective neurons and the LFP during short-categorized trials, and between longselective neurons and the LFP during long-categorized trials: the peak frequency reflected the categorical decision. (b) Same for preSMA: there were no significant peaks in the beta range.
3. The authors claim that the results are the same for the temporal and spatial tasks, but all spectra shown in the main figures are collapsed across both tasks. There seems to be some information about the estimated peak parameters for the individual tasks in the supplementary tables (unclear, due to use of shorthands for the conditions which are not defined), but this is not sufficient to evaluate the effects. Please show separate spectra for the two tasks.
We apologize for the lack of clarity in showing the data from the individual tasks. We have now clarified our usage of the shorthand terms in the table captions (T1, T2, T3 are the interval categorization tasks with the shortest to longest intervals respectively; similarly, S1, S2, S3 are the distance categorization tasks with shortest to longest distances respectively). We now have also included figures showing the spectra for the separate tasks. Figure S1. Beta peak frequency in monkey 1 dlPFC reflected the categorical decision during the decision delay in each version of the task. Power spectra for "long" stimulus (blue) vs. "short" stimulus trials (orange) during trials with correct responses (ac) in the temporal categorization versions of the task with the shortest to longest stimuli respectively, and (d) the distance categorization task (see Figure 1b for exact values and Table 4 for statistics). Shaded regions around the line graphs represent the standard error of the mean. Figure S2. Beta peak frequency in monkey 1 preSMA reflected the categorical decision during the decision delay in each version of the task. Power spectra for "long" stimulus (blue) vs. "short" stimulus trials (orange) during trials with correct responses (ac) in the temporal categorization versions of the task with the shortest to longest stimuli respectively, and (d) the distance categorization task (see Figure 1b for exact values and Table 5 for statistics). Shaded regions around the line graphs represent the standard error of the mean. Figure S3. Beta peak frequency in monkey 2 preSMA reflected the categorical decision during the decision delay in each version of the task. Power spectra for "long" stimulus (blue) vs. "short" stimulus trials (orange) during trials with correct responses (a) in the temporal categorization versions of the task (pooled together) and (d) the distance categorization versions of the task (pooled together; see Figure 1b for exact stimulus values and Table 5 for statistics). Shaded regions around the line graphs represent the standard error of the mean.